财务管理第五章风险和收益精选ppt

Chapter5,RiskandReturn,Glossary,StandardDeviation标准差或者标准离差Expectedreturn期望回报率Normaldistribution正态分布Coefficientofvariation离差系数variance方差ContinuousDistributions连续分布discretedistribution离散分布CertaintyEquivalent(CE)资本回收保证量RiskPreference风险偏好RiskIndifference风险中立RiskAversion风险规避TheCapitalAssetPricingModel(CAPM)资本资产定价模型SystematicRisk系统风险UnsystematicRisk非系统风险,DefiningReturn,Incomereceivedonaninvestmentplusanychangeinmarketprice,usuallyexpressedasapercentofthebeginningmarketpriceoftheinvestment.,Dt+(Pt-Pt-1),Pt-1,R=,ReturnExample,ThestockpriceforStockAwas$10pershare1yearago.Thestockiscurrentlytradingat$9.50pershare,andshareholdersjustreceiveda$1dividend.Whatreturnwasearnedoverthepastyear?,ReturnExample,ThestockpriceforStockAwas$10pershare1yearago.Thestockiscurrentlytradingat$9.50pershare,andshareholdersjustreceiveda$1dividend.Whatreturnwasearnedoverthepastyear?,$1.00+($9.50-$10.00),$10.00,R=,=5%,DefiningRisk,Greaterthevariability,theriskierthesecurityissaidtobe,Thevariabilityofreturnsfromthosethatareexpected.,DeterminingExpectedReturn(DiscreteDist.),R=S(Ri)(Pi)Ristheexpectedreturnfortheasset,Riisthereturnfortheithpossibility,Piistheprobabilityofthatreturnoccurring,nisthetotalnumberofpossibilities.,n,i=1,HowtoDeterminetheExpectedReturnandStandardDeviation,StockBWRiPi(Ri)(Pi)-.15.10-.015-.03.20-.006.09.40.036.21.20.042.33.10.033Sum1.00.090,Theexpectedreturn,R,forStockBWis.09or9%,DeterminingStandardDeviation标准差或者标准离差(RiskMeasure),n,i=1,s=S(Ri-R)2(Pi)StandardDeviation,s,isastatisticalmeasureofthevariabilityofadistributionarounditsmean.Itisthesquarerootofvariance(方差）.Note,thisisforadiscretedistribution（离散分布）.,HowtoDeterminetheExpectedReturnandStandardDeviation,StockBWRiPi(Ri)(Pi)(Ri-R)2(Pi)-.15.10-.015.00576-.03.20-.006.00288.09.40.036.00000.21.20.042.00288.33.10.033.00576Sum1.00.090.01728,DeterminingStandardDeviation(RiskMeasure),s=S(Ri-R)2(Pi)s=.01728s=.1315or13.15%,n,i=1,CoefficientofVariation,Theratioofthestandarddeviationofadistributiontothemeanofthatdistribution.ItisameasureofRELATIVErisk.CV=s/RCVofBW=.1315/.09=1.46,Discretevs.ContinuousDistributions连续分布,DiscreteContinuous,DeterminingExpectedReturn(ContinuousDist.),R=S(Ri)/(n)Ristheexpectedreturnfortheasset,Riisthereturnfortheithobservation,nisthetotalnumberofobservations.,n,i=1,DeterminingStandardDeviation(RiskMeasure),n,i=1,s=S(Ri-R)2(n)Note,thisisforacontinuousdistributionwherethedistributionisforapopulation.Rrepresentsthepopulationmeaninthisexample.,ContinuousDistributionProblem,Assumethatthefollowinglistrepresentsthecontinuousdistributionofpopulationreturnsforaparticularinvestment(eventhoughthereareonly10returns).9.6%,-15.4%,26.7%,-0.2%,20.9%,28.3%,-5.9%,3.3%,12.2%,10.5%CalculatetheExpectedReturnandStandardDeviationforthepopulationassumingacontinuousdistribution.,LetsUsetheCalculator!,Enter“Data”first.Press:2ndData2ndCLRWork9.6ENTER-15.4ENTER26.7ENTERNote,weareinputtingdataonlyforthe“X”variableandignoringentriesforthe“Y”variableinthiscase.,LetsUsetheCalculator!,Enter“Data”first.Press:-0.2ENTER20.9ENTER28.3ENTER-5.9ENTER3.3ENTER12.2ENTER10.5ENTER,LetsUsetheCalculator!,ExamineResults!Press:2ndStatthroughtheresults.Expectedreturnis9%forthe10observations.Populationstandarddeviationis13.32%.Thiscanbemuchquickerthancalculatingbyhand,butslowerthanusingaspreadsheet.,CertaintyEquivalent(CE)资本回收保证量istheamountofcashsomeonewouldrequirewithcertaintyatapointintimetomaketheindividualindifferentbetweenthatcertainamountandanamountexpectedtobereceivedwithriskatthesamepointintime.,RiskAttitudes,CertaintyequivalentExpectedvalueRiskPreference风险偏好Certaintyequivalent=ExpectedvalueRiskIndifference风险中立CertaintyequivalentExpectedvalueRiskAversion风险规避MostindividualsareRiskAverse.,RiskAttitudes,RiskAttitudeExample,Youhavethechoicebetween(1)aguaranteeddollarrewardor(2)acoin-flipgambleof$100,000(50%chance)or$0(50%chance).Theexpectedvalueofthegambleis$50,000.Maryrequiresaguaranteed$25,000,ormore,tocalloffthegamble.Raleighisjustashappytotake$50,000ortaketheriskygamble.Shannonrequiresatleast$52,000tocalloffthegamble.,WhataretheRiskAttitudetendenciesofeach?,RiskAttitudeExample,Maryshows“riskaversion”becauseher“certaintyequivalent”theexpectedvalueofthegamble.,RP=S(Wj)(Rj)RPistheexpectedreturnfortheportfolio,Wjistheweight(investmentproportion)forthejthassetintheportfolio,Rjistheexpectedreturnofthejthasset,misthetotalnumberofassetsintheportfolio.,DeterminingPortfolioExpectedReturn,m,j=1,DeterminingPortfolioStandardDeviation,m,j=1,m,k=1,sP=SSWjWksjkWjistheweight(investmentproportion)forthejthassetintheportfolio,Wkistheweight(investmentproportion)forthekthassetintheportfolio,sjkisthecovariancebetweenreturnsforthejthandkthassetsintheportfolio.,WhatisCovariance协方差?,sjk=sjskrjksjisthestandarddeviationofthejthassetintheportfolio,skisthestandarddeviationofthekthassetintheportfolio,rjkisthecorrelationcoefficientbetweenthejthandkthassetsintheportfolio.,CorrelationCoefficient,Astandardizedstatisticalmeasureofthelinearrelationshipbetweentwovariables.Itsrangeisfrom-1.0(perfectnegativecorrelation),through0(nocorrelation),to+1.0(perfectpositivecorrelation).,Variance-CovarianceMatrix,Athree-assetportfolio:Col1Col2Col3Row1W1W1s1,1W1W2s1,2W1W3s1,3Row2W2W1s2,1W2W2s2,2W2W3s2,3Row3W3W1s3,1W3W2s3,2W3W3s3,3sj,k=isthecovariancebetweenreturnsforthejthandkthassetsintheportfolio.,YouarecreatingaportfolioofStockDandStockBW(fromearlier).Youareinvesting$2,000inStockBWand$3,000inStockD.RememberthattheexpectedreturnandstandarddeviationofStockBWis9%and13.15%,respectively.TheexpectedreturnandstandarddeviationofStockDis8%and10.65%,respectively.ThecorrelationcoefficientbetweenBWandDis0.75.Whatistheexpectedreturnandstandarddeviationoftheportfolio?,PortfolioRiskandExpectedReturnExample,DeterminingPortfolioExpectedReturn,WBW=$2,000/$5,000=.4WD=$3,000/$5,000=.6RP=(WBW)(RBW)+(WD)(RD)RP=(.4)(9%)+(.6)(8%)RP=(3.6%)+(4.8%)=8.4%,Two-assetportfolio:Col1Col2Row1WBWWBWsBW,BWWBWWDsBW,DRow2WDWBWsD,BWWDWDsD,DThisrepresentsthevariance-covariancematrixforthetwo-assetportfolio.,DeterminingPortfolioStandardDeviation,Two-assetportfolio:Col1Col2Row1(.4)(.4)(.0173)(.4)(.6)(.0105)Row2(.6)(.4)(.0105)(.6)(.6)(.0113)Thisrepresentssubstitutionintothevariance-covariancematrix.,DeterminingPortfolioStandardDeviation,Two-assetportfolio:Col1Col2Row1(.0028)(.0025)Row2(.0025)(.0041)Thisrepresentstheactualelementvaluesinthevariance-covariancematrix.,DeterminingPortfolioStandardDeviation,DeterminingPortfolioStandardDeviation,sP=.0028+(2)(.0025)+.0041sP=SQRT(.0119)sP=.1091or10.91%AweightedaverageoftheindividualstandarddeviationsisINCORRECT.,DeterminingPortfolioStandardDeviation,TheWRONGwaytocalculateisaweightedaveragelike:sP=.4(13.15%)+.6(10.65%)sP=5.26+6.39=11.65%10.91%=11.65%ThisisINCORRECT.,StockCStockDPortfolioReturn9.00%8.00%8.64%Stand.Dev.13.15%10.65%10.91%CV1.461.331.26TheportfoliohastheLOWESTcoefficientofvariationduetodiversification.,SummaryofthePortfolioReturnandRiskCalculation,Combiningsecuritiesthatarenotperfectly,positivelycorrelatedreducesrisk.,DiversificationandtheCorrelationCoefficient,INVESTMENTRETURN,TIME,TIME,TIME,SECURITYE,SECURITYF,CombinationEandF,SystematicRiskisthevariabilityofreturnonstocksorportfoliosassociatedwithchangesinreturnonthemarketasawhole.UnsystematicRiskisthevariabilityofreturnonstocksorportfoliosnotexplainedbygeneralmarketmovements.Itisavoidablethroughdiversification.,TotalRisk=SystematicRisk+UnsystematicRisk,TotalRisk=SystematicRisk+UnsystematicRisk,TotalRisk=SystematicRisk+UnsystematicRisk,TotalRisk,Unsystematicrisk,Systematicrisk,STDDEVOFPORTFOLIORETURN,NUMBEROFSECURITIESINTHEPORTFOLIO,Factorssuchaschangesinnationseconomy,taxreformbytheCongress,orachangeintheworldsituation.,TotalRisk=SystematicRisk+UnsystematicRisk,TotalRisk,Unsystematicrisk,Systematicrisk,STDDEVOFPORTFOLIORETURN,NUMBEROFSECURITIESINTHEPORTFOLIO,Factorsuniquetoaparticularcompanyorindustry.Forexample,thedeathofakeyexecutiveorlossofagovernmentaldefensecontract.,CAPMisamodelthatdescribestherelationshipbetweenriskandexpected(required)return;inthismodel,asecuritysexpected(required)returnistherisk-freerateplusapremiumbasedonthesystematicriskofthesecurity.,CapitalAssetPricingModel(CAPM),1.Capitalmarketsareefficient.2.Homogeneousinvestorexpectationsoveragivenperiod.3.Risk-freeassetreturniscertain(useshort-tointermediate-termTreasuriesasaproxy代理).4.Marketportfoliocontainsonlysystematicrisk(useS&P500Indexorsimilarasaproxy).,CAPMAssumptions,CharacteristicLine,EXCESSRETURNONSTOCK,EXCESSRETURNONMARKETPORTFOLIO,Beta=,RiseRun,Narrowerspreadishighercorrelation,CharacteristicLine,Calculating“Beta”onYourCalculator,TheMarketandMyStockreturnsare“excessreturns”andhavetherisklessratealreadysubtracted.,Calculating“Beta”onYourCalculator,Assumethatthepreviouscontinuousdistributionproblemrepresentsthe“excessreturns”ofthemarketportfolio(itmaystillbeinyourcalculatordataworksheet-2ndData).Entertheexcessmarketreturnsas“X”observationsof:9.6%,-15.4%,26.7%,-0.2%,20.9%,28.3%,-5.9%,3.3%,12.2%,and10.5%.Entertheexcessstockreturnsas“Y”observationsof:12%,-5%,19%,3%,13%,14%,-9%,-1%,12%,and10%.,Calculating“Beta”onYourCalculator,Letusexamineagainthestatisticalresults(Press2ndandthenStat)Themarketexpectedreturnandstandarddeviationis9%and13.32%.Yourstockexpectedreturnandstandarddeviationis6.8%and8.76%.TheregressionequationisY=a+bX.Thus,ourcharacteristiclineisY=1.4448+0.595Xandindicatesthatourstockhasabetaof0.595.,Anindexofsystematicrisk.Itmeasuresthesensitivityofastocksreturnstochangesinreturnsonthemarketportfolio.Thebetaforaportfolioissimplyaweightedaverageoftheindividualstockbetasintheportfolio.,WhatisBeta?,CharacteristicLinesandDifferentBetas,EXCESSRETURNONSTOCK,EXCESSRETURNONMARKETPORTFOLIO,Beta1(aggressive),Eachcharacteristiclinehasadifferentslope.,Rjistherequiredrateofreturnforstockj,Rfistherisk-freerateofreturn,bjisthebetaofstockj(measuressystematicriskofstockj),RMistheexpectedreturnforthemarketportfolio.,SecurityMarketLine,Rj=Rf+bj(RM-Rf),SecurityMarketLine,Rj=Rf+bj(RM-Rf),bM=1.0SystematicRisk(Beta),Rf,RM,RequiredReturn,RiskPremium,Risk-freeReturn,LisaMilleratBasketWondersisattemptingtodeterminetherateofreturnrequiredbytheirstockinvestors.Lisaisusinga6%Rfandalong-termmarketexpectedrateofreturnof10